Conduction of heat exchange fluids

ABSTRACT

The heat transfer between a tube and a fluid therein is to be enhanced by providing a tube with helical corrugation having axial crest-to-crest spacing T, crest-to-valley height t, inner diameter d and pitch angle of the helix delta . These parameters are selected as follows: t/5 from 0.01 to 0.5, preferably between 0.1 and 0.2; T/d from 0.01 to 1.0, preferably between 0.03 and 0.3 and helix angle delta from 5* to 20*.

United States Patent [11] 3,817,319 Kauder June 18, 1974 41 CONDUCTIONOF HEAT EXCHANGE FLUIDS lnventor: Knut Kauder, Krahenbruch,

Germany Kabel-und Metallwerke Gutehoffnungshutte Aktiengesellschaft,Hannover, Germany Filed: Nov. 14, 1972 Appl. No.: 306,181

Assignee:

Foreign Application Priority Data Nov. 15, 1971 Germany 2156578 US. Cl165/1, 165/181 Int. Cl F28f l/20 Field of Search 165/], 147, 179, 181

[56] References Cited UNITED STATES PATENTS 3,612,175 10/1971 Ford etal. 165/179 Primary Examiner-Charles Sukalo Attorney, Agent, orFirm-Ralf H. Siegemund [5 7] ABSTRACT The heat transfer between a tubeand a fluid therein is to be enhanced by providing a tube with helicalcorrugation having axial crest-to-crest spacing T, crest-tovalley heightI, inner diameter d and pitch angle of the helix 8. These parameters areselected as follows: /5 from 0.01 to 0.5, preferably between 0.1 and0.2; T/d from 0.01 to 1.0, preferably between 0.03 and 0.3 and helixangle 6 from 5 to 20.

6 Claims, 7 Drawing Figures PATENTEBJuu 18 I974 'sumlnis 0;, f mm M 6 wC CONDUCTION OF HEAT EXCHANGE FLUIDS BACKGROUND OF THE INVENTION Thepresent invention relates to the conduction of fluid through flexibletubes, particularly for purposes of heat exchange. More particularly,the invention relates to improvements involving particulars of helicalcorrugation for such tubes, with regard to flow characteristics inrelation to the tubes wall.

Many fields of art employ tubes which can be described as having wallstructure of a regularly repeated geometric contour and configurationpattern. Depending on various factors, including particulars of thepattern, such tubes can be stiff or flexible. However, the tube will bequite flexible where its corrugation crests and valleys loop around theaxis and the wall of the tube is not too thick. Tubing with corrugationthat loops around the axis along the periphery of the tube, is quiteflexible and can be reeled on drums. In fact, the tubing can beinstalled just like a cable. Such tubes are used as conduit for fluids,either for transporting fluid as such or for using the fluid medium ascarrier for thermal energy. Short, metal hose, as well as tubes ofmedium length, are used particularly in case of heat exchange betweenthe fluid in the tube and the environment, e.g. over the length of thetubing or at the destination point. Long corrugated tubing is used asconduit for fresh or waste water or as conduit for hot water or steam ina central heating system, or for many other purposes. The demand fortubing of this type has steadily increased in recent years. However,corrugated tubes have not always been found satisfactory as carrier fora fluid in a heat exchange device.

A condition is posed usually in the field of heat exchange that thefluids undergoing heat exchange must not come into direct mutualcontact, as they should not mix. Thus, tubes are used for heat transferfrom one fluid to another one, which tubes maintain physical separationof the fluids but permit heat transfer over short distances of flow. Forexample, a concentric tube system establishes a flow path for one fluidin an inner tube, while the other fluid passes through the ring spacebetween inner and outer tube. Heat is transferred through the wall ofthe inner tube.

Considering the heat exchange process in some detail, it involvesbasically three steps. (1) heat is transferred from the warmer fluid tothe surface of the wall separating the fluids, (2) heat is conductedthrough the wall, (3) heat is transferred from the other wall surface tothe cooler fluid. If the wall is made, for example, of copper or anyother material having a high coefficient of thermal conductance, thethermal conductance through the wall can be disregarded in theconsideration of the overall heat transmission between the two fluids.

In case of a tube, having inner diameter di, outer diameter do, andlength L, the surface areas involved in 'the transfer are A, 'rr L difor the inner surface and A 1r L do for the outer surface. Let a, and01,, be respectively the transfer coefficients at inner and outersurfaces, then the following relation describes the thermal transmissionprocess.

i i' o au i i' o o) (I) wherein K is the particular coefficient of heattransmission, and A is defined by A 1r L (do di)/(lognat do/di) 2 Thefraction in the equation being the logarithmic median value for the tubes diameter.

Equation l teaches that the heat transmission coefficient is alwayssmaller than the smallest heat transfer coefficient a of the systembecause the equation can be written so that such smallest coefficient(a,- or 04,) appears as being multiplied by a factor that is necessarilysmaller than unity. The heat transfer coefficients, of course, includethe thermal properties of the materials involved. Moreover, thecoefficients a are composite parameters which in each system: fluid-wallsurface, combine all physical processes that transfer thermal energyfrom the fluid to the wall (or vice versa). Such processes includemolecular conduction, convection, radiation and evaporation orcondensation. Evaporation and condensation occur only in special cases.Molecular conduction and radiation are usually determined by thephysical properties of the materials involved. The variable parameter inthe process is convection, whereby convection is to be understoodgenerally as any flow in any of the fluids which contribute to heattransfer.

In analogy to the known expedient of increasing the effective heatexchange surface, it is, for example, known to place baffles into asmooth wall tube. The baffles differ as to cross section. The baffles soplaced in smooth wall tubes may even have rectangular contour, or arediscs or rings, or have propeller-like or helical configuration. Forsimilar Reynolds number one can increase heat transfer to about theeightfold value, but up to a ten-thousandfold increase in pressure lossis suffered under such conditions. Thus, the advantage of a better heattransmission process is at least partially offset by high pressurelosses requiring increased pumping output.

DESCRIPTION OF THE INVENTION It is an object of the present invention toimprove flow conditions in (or on) a tube so as to improve the heattransfer as between fluid and tube wall surface, in either direction andon either side of the tube.

In accordance with the preferred embodiment of the invention, it issuggested to use helically corrugated tubing wherein the ratio ofcorrugation crest-to-valley height (radial) and corrugationcrest-to-crest (axial) distance is from 0.01 to 0.5, preferably from 0.1to 0.2; the ratio of the crest-to-valley height to smallest innerdiameter of the tube is to be about 0.01 to 1.0 and the angle of thecorrugation helix is to be between 5 to 20.

The known devices for improving convection are essentially devices whichinduce and enhance tubulent flow; the more turbulent flow the higher isthe heat transfer across the flow into the boundary surface. Thepenalty, of course, is pressure loss because turbulence enhances both,transfer of momentum and transfer of thermal energy.

Unlike these known methods, applicant suggests to use a tube whichimparts rotation upon the flow as a whole. The rotation being defined asthe product of circumferential speed and circumference divided by twicethe cross section area of the tube. Thus, rotation as defined increaseswith increasing the product of the speed and the circumference and byreducing the cross section.

As a viscous fluid flows through a tube with helical boundary channels,helical flow adjacent the boundary tends to impart rotation upon thecylindrical, straight axial center flow. Accordingly, the flow has twocomponents, axial and circumferential. The intensity of the lattercomponent depends upon the configuration of the helical channel as itinduces, ultimately, the circumferential velocity component. Theintensity of the induction of that rotational flow will be higher forlarger crest-to-valley height of the corrugation (channel depth). Therotational flow will be lower, the larger is the axial spacing ofcorrugation crests. Thus, rotational flow will be determined by theratio of these geometric values as defining the corrugation as well asby the relative channel depth and the pitch of the helix.

DESCRIPTION OF THE DRAWINGS While the specification concludes withclaims particularly pointing out and distinctly claiming the subjectmatter which is regarded as the invention, it is believed that theinvention, the objects and features of the invention and furtherobjects, features and advantages thereof will be better understood fromthe following description taken in connection with the accompanyingdrawings in which:

FIG. 1 is a three-dimensional velocity profile diagram in a tube to beproduced for heat exchange enhancement;

FIGS. 2a and 2b are longitudinal and cross-sectional views through acorrugated tube;

FIGS. 3 and 4 are diagrams for showing kinetic energy of rotational flowand axial flow plotted against corrugation defining tube parameters;

FIG. 5 shows a tube to be used as fluid conduit; and

FIG. 6 is a schematic section diagram through a corrugation valley andadjoining crests to define contour of helical channel flow along a tubeswall.

Proceeding now to the detailed description of the drawings, FIG. 1illustrates the velocity profile 15 to be attained. The profile isplotted in three-dimensional diagram. The horizontal plane shown inperspective view is taken in a cross section through a tube, using thesame plane to plot azimuthal velocity C along a diameter 10, includingcircumferential velocity component C,,,,*. The resulting profile curveis denoted with 11.

The axial velocity is plotted along a vertical axis of the drawing,using said diameter 10 as base for each velocity vector. The end pointsof the vectors follow a profile 12 for the axial component of fluidvelocity. The character c denotes a vector on that diameter as footpoint of the actual composite velocity resulting in a profile curve 15.

This then is the velocity distribution found desirable. That thisdistribution improves, in fact, the heat transfer between fluid andboundary will be justified next, the generation of that profile will bediscussed thereafter.

The fluid flow in a tube according to the profile 15 causestransportation of kinetic energy and momentum in accordance with densityand velocity. That energy transport can be divided into an axialcomponent and an azimuthal or rotational component. The relative energyinherent in the axial component of flow and integrated over the crosssection of the conduit, may be designated E and the rotationalcomponent, integrated analogously, may be called E Fluid incrementscarrying this kinetic energy of flow are also the carrier of the thermalenergy. Thus, a high energy component for the rotational (kinetic) flowinherently enhances the heat transfer into the wall. Therefore, thefluid flows in axial direction pursuant to the regular axial extensionof the conduit; a rotational velocity field is superimposed upon theaxial component, circulating around the circumference and imparting itsthermal energy to (or receiving thermal energy from) the wall of thetube.

The mechanism for setting up the rotational flow of the type plotted inFIG. 1 is explained now with reference to FIG. 2. The FIG. shows a tubemade, for example, from thin metal strip. The strip has been foldedlongitudinally into a split tube, the joint being established by andalong the previously opposite edges of the strip which now abut oroverlap. The joint is closed through longitudinal seam welding, and theresulting tube is provided with helical corrugation. The corrugation incross section appears as a wave-like pattern of alternating crests andgrooves or valleys. Corrugated tubing is, of course, known per se, butthe corrugation is provided under observation of specific rules so thatthe rotational component of flow is obtained by forcing the fluid tofollow particular channels as defined by the corrugation grooves orvalleys as seen from the interior of the tube.

The (axial) crest-to-crest distance T and the (internal, radial)crest-to-valley height I define the corrugation pattern. Of furtherrelevancy is the smallest inner diameter d which is the diameter of acylinder 20 that is tangent to all inwardly directed crests. T/n'ddefines the tangent function of the helix angle 5 of the corrugation.

The largest outer diameter D of the tube, measured on a cylinder 21, istangent to the outer apeces of the radially outwardly directed crests.If the tubes wall has thickness S, one can also define a cylinder thatis tangent to the apex of the inner valleys, that cylinder has diameterD-2S.

In order to practice the invention, the parameters are selected asfollows. For t/T to range from 0.01 to 0.5 (preferably 0.1 to 0.2); t/dto be within the range from 0.01 to 1.0 (preferably 0.03 to 0.3); andhelix angle 8 5 to 20. It can readily be seen that these corrugationparameters define the intensity of compelling a peripheral portion ofthe fluid to flow in a helical channel, and viscosity causes the fluidoutside of the helical channel, closer to the interior of the tube, tostill have a rotational component. The parameters determine also thenumber of loops in the flow path per axial unit length.

FIG. 3 illustrates the relationship between corrugation helix angle 8and the ratio of the two kinetic energies E and E as defined above. Thesolid dots are measured values for !/d= 0.0455, the circles have beenmeasured for t/d 0.635. The angle 8 has to be varied through variationof T, and curve 30 has been calculated.

FIG. 4 illustrates the energy ratio E /E, plotted against t/d for T/d0.3 which is between 5 and 6. As stated, it was found in practice thatfor best results t/T 0.1 to 0.2 and t/d= 0.03 to 0.3. This way oneobtains best conditions for heat transfer as between fluid and wall, sothat these parameters are deemed preferred for heat exchange tubing. Asthe channel flow includes a rotational component, little actual pressureloss occurs as a result of this deviation from straight axial flow,because rotational flow (ideally) produces no pressure gradient.

The preferred form of constructing a heat exchange tube is actuallyshown in FIG. 5. FIG. 2 has served primarily for defining the relevantparameters. The grooves or valleys in FIG. 5 are rather shallow,followed in each instance by a pronounced crest. The selection of tubecorrugation is preferably tightened additionally as follows.

The corrugation has been described in terms of the parameters T, t andd. However, this does not completely described the corrugation contouras can readily be seen by comparing FIGS. 2 and 5. FIG. 6 showsparticularly a variety of curves, each outlining the corrugation for thesame set of parameters T, t and d, including even an asymmetric patternas shown-in dotted lines. Not all of these contours give equallyfavorable results. It can readily be seen that, for example, trace aoutlines a corrugation which, in fact, establishes a deep, narrowchannel separated by crests with rather shallow apex as extending intothe flow, so that a predominant portion of the inner surface is definedby almost cylindrical sections, separated by the narrow spiral channel.On the other hand, trace b outlines a contour of a rather wide channelseparated axially by steep ridges (such as shown in FIG. 5).

It was found that best results are obtained if the channel area isselected as follows. One can see that wavelength T/2 and corrugationdepths t define a rectangle. Part of this rectangle is occupied by twosubareas, each being half of a cross section area of an inwardlydirected corrugation crest (e.g., as hatched), the remainder being thechannel cross section area. That area is to be about two-thirds less ofthe rectangle T/2-t. To state it differently, half of the cross sectionof the helical channel as defined by the corrugation, is at most twiceas large as half of the cross section of the helical ridge thatseparates the loops of the spiral channel. Under these conditions,optimum heat transfer coeffi cients are obtained as between fluid andthe tubes wall. This is approximately curve c in FIG. 6.

Tubes meeting these requirements are well suited as fluid conductors inlong paths for heat exchange such as required, for example, indesalination plants. It may be desirable here to provide stretches ofthe tube with smooth wall to facilitate installation in heat exchangeplanes.

It should also be mentioned that the helical corrugation having thestated parameters do, in fact, provide for rotational flow at optimumheat transfer characteristics as been fluid and wall. Tubes havingannular corrugation at similar parameters provide baffles in the flowresulting in backwater zones adjacent the annular corrugation ridgeswith no rotational flow and provide for considerably inferior heattransfer.

The invention is not limited to the embodiments described above but allchanges and modifications thereof not constituting departures from thespirit and scope of the invention are intended to be included.

1 claim:

1. Method for conducting fluids through a tube for heat transfer asbetween tube and fluid. comprising the step of:

using a helically corrugated tube;

the corrugation having axially alternating crests and valleys;

the axial distance T from crest-to-crest, the crest-tovalley t, theinner tube diameter d and the helix angle 8 of the corrugation selectedso that t/T is from 0.01 to 0.5, t/d from 0.01 to 1.0; and 8 from 5 to20.

2. Method as in claim 1, wherein t/T is from 0.1 to 0.2.

3. Method as in claim 1, wherein t/d is from 0.03 to 0.3.

4. Method as in claim 1, wherein t/Tis from 0.1 to 0.2 and t/d from 0.03to 0.3.

5. Method as in claim 1, wherein half the cross section of a fluidflowchannel defined by the helical corrugation valleys is not larger thantwice half of the cross section of the crests as separating axiallysequential channel loops.

6. Method as in claim 1, using the tube in a heat exchanger.

1. Method for conducting fluids through a tube for heat transfer asbetween tube and fluid, comprising the step of: using a helicallycorrugated tube; the corrugation having axially alternating crests andvalleys; the axial distance T from crest-to-crest, the crest-to-valleyt, the inner tube diameter d and the helix angle delta of thecorrugation selected so that t/T is from 0.01 to 0.5, t/d from 0.01 to1.0; and delta from 5* to 20*.
 2. Method as in claim 1, wherein t/T isfrom 0.1 to 0.2.
 3. Method as in claim 1, wherein t/d is from 0.03 to0.3.
 4. Method as in claim 1, wherein t/T is from 0.1 to 0.2 and t/dfrom 0.03 to 0.3.
 5. Method as in claim 1, wherein half the crosssection of a fluid flow channel defined by the helical corrugationvalleys is not larger than twice half of the cross section of the crestsas separating axially sequential channel loops.
 6. Method as in claim 1,using the tube in a heat exchanger.